Konike

master's thesis

• Title (english): Conics
• Author: Iva Smolić
• Mentor: Tomislav Pejković (mentor)
• Committee member: Tomislav Pejković (predsjednik povjerenstva)
• Committee member: Aleksandra Čižmešija (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-03-02, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Konike ili čunjosječnice su algebarske ravninske krivulje drugoga reda nastale presjekom ravnine i stožaste plohe. To su kružnica, elipsa, parabola i hiperbola, te njihove degeneracije, koje u ovom radu općenito nismo uzimali u obzir. Ovaj diplomski rad podijeljen je u četiri poglavlja. U prvom poglavlju naveli smo temeljne pojmove i tvrdnje potrebne za razumijevanje daljnjeg rada i dokaza. U drugom poglavlju su za svaku krivulju navedena neka osnovna svojstva i definicije te različiti oblici jednadžbi. U trećem poglavlju iskazali smo i dokazali zrcalno te izogonalno svojstvo konika, dok smo u posljednjem poglavlju naveli još neka važna svojstva i teoreme o konikama. Dokazi tvrdnji provedeni su bez korištenja analitičke i projektivne geometrije.

Abstract (english)

Conics are algebraic plane curves of the second degree formed by the intersection of a plane and a double cone. These are the circle, ellipse, parabola and hyperbola, and their degenerations, which we generally do not take into account in this thesis. This Master’s thesis is divided into four chapters. In the first one we introduce notions and statements needed in the thesis. In the second chapter we present some basic properties and definitions for each curve and different forms of their equations. In the third chapter, we state and prove the mirror and isogonal properties of conics, while in the last chapter we give some additional important properties and theorems about conics. The proofs of the statements are carried out without using analytic and projective geometry.

• Keywords: čunjosječnice; algebarske ravninske krivulje drugoga reda; kružnica; elipsa; parabola; hiperbola
• Keywords (english): algebraic plane curves of the second degree; circle; ellipse; parabola; hyperbola
• Language: croatian
• URN:NBN: urn:nbn:hr:217:482259
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-08-18 10:43:10